CRYSTALLOGRAPHY

INTRUDUCTION: Mineralogy is the branch of science dealing with the study of

minerals. Nowdays a mineral is defined as A geological body, occurring in the
inorganic mature and possesses a certain characteristic atomic structure which is
expressed in its crystalline form, physical properties and chemical homogeneity.
- In our course of Mineralogy and Crystallography we are going to deal with the
internal atomic structure of minerals which is closely related to the study of
their external form of their crystals (Crystallography), their physical properties
( Chemical Mineralogy) and their optical properties (optical Mineralogy).
- Formation of crystal: A crystal is a solid body bounded by plane. Natural
surfaces (crystal faces), which are the external expression of a regular internal
arrangement of constituent atoms or ions.
- The study of the arrangement of atoms within a crystal, that is, of atomic
structure, has been made in recent years by x-ray analysis.
- The smallest complete unit of the three dimensional pattern- which is repeated
through the crystal- is called the unit cell.

The whole pattern or from of the external crystal form is formed by stacking unit cells
together. To take a simple example, in crystals of sodium chloride (Halite) the atoms
of Na and Cl are arranged at the corners of a series of cubes, as shown in (Fig. 1).



- The unit cell of sodium chloride contains four atoms of Na and four of Cl,
whose arrangement is exactly similar to that in every other unit cell of the
substance.







- It is to be noted that the number of atoms in the unit cell of a particular
minerals is not necessarily the same as in its formula, but is usually some
simple multiple; for NaCl; this multiple is four.
- Space Lattice: Naturally the atoms of the different elements that enter in the
composition of a mineral or its crystal are arranged together in a regular three
dimensional pattern containing their unit cells in an arrangement called "space
lattice".
- The space lattice formed by points in space. Each lattice point represents the
center of gravity of an ion, atom or molecule which occupies a similar
surrounding.


linear pattern



two dimensional pattern

Three
dimensional pattern












The 14 Three-Dimensional Bravais Lattices
1. Primitive Triclinic

C-centered are no constraints on axial lengths or on b. The standard choice of axes is
that b is unique. The centered cell is also unique and preserves the axis identities and
has an additional lattice point at 1/2+x, 1/2+y, z, so that there is an additional lattice
point per cell for a total of two, whereas the primitive cell have just one lattice point
per cell (eight corners, each of which is 1/8th within the cell). Because there are
several possible choices of the a and b axes, it is possible to choose an A- centered or
I-centered cell. It is possible to show that centering of any other face reduces to one of
these two.

4. & 5. Primitive C-centered Primitive and C-centered orthorhombic. alpha = beta
gamma = 90. There are no constraints on axial lengths. Labeling of axes is arbitrary.
Just as in the monoclinic case, the centered cell preserves the axis orthogonality and
has an additional lattice point at 1/2+x, 1/2+y, z. It would also be possible to choose
equivalent A or B centered cell, but conventionally c is the centered axis.

6 & 7. I-centered F-centered centered (body-centered) cell has an additional lattice
point at 1/2+x, 1/2+y, 1/2+z, for a total of two points per cell. In the F-centered cell
each of the faces contains 1/2 of an additional lattice point for a total of four per cell.
In each, the labeling of axes is arbitrary.


8 & 9. Primitive I-centered Primitive and I-centered Tetragonal alpha = beta = gamma
= 90 degrees. a = b; and c is unique axis with 4 or -4 symmetry. The I- centered
(body-centered) cell has an additional lattice point at 1/2+x, 1/2+y, 1/2+z, for a total
of two points per cell. Note that there is no C-centered tetragonal cell be cause it
would be possible to choose a primitive tetragonal cell with half the volume. Similarly
an F-centered cell would reduce to an I-centered cell.
10 & 11. Primitive I-centered Primitive and I-centered Cubic (Isometric) alpha = beta
= gamma = 90 a = b = c. These are similar to the above except for the additional
axial length constraint.
12. F-centered Face Centered Cubic (Isometric) alpha = beta = gamma = 90 a = b =
c. Each of the six faces contains a lattice point for a total of four per cell.
13. 120 120 Primitive R-centered Primitive Hexagonal
The R-centered cell contains lattice points at 1/3 and 2/3 along the body diagonal.
This makes it pos sible to choose an alternative primitive cell such that alpha = beta =
gamma, but not 90 or 120 degrees.

- CRYSTAL SYMMETRY: (External elements of symmetry)
The fundamental symmetry operations are: (1) rotation about an axis (2)
reflection across a plane (3) rotation about an axis combined with inversion (rotary
inversion). (4) Inversion about a center alone is considered as 1- fold axis of rotary
inversion.
(1) Rotation axis: The rotation axis is an imaginary line through a crystal about
which the crystal about which the crystal may be rotated and repeat itself-in
appearance two or more times during
a complete rotation. The nature of crystals is
such that no symmetry axes other than
1-, 2-, 3-, 4-, and 6- fold can exist (fig. 3).
Axis of Rotation = imaginary line through a crystal about which the crystal may be
rotated and repeat itself in appearance (1,2,3,4 or 6 times during a complete rotation).
Permissible rotations - Proper

1-fold 360 I Identity

2-fold 180 2

3-fold 120 3

4-fold 90 4

6-fold 60 6


(2) Mirror plane: A mirror or symmetry plane is an imaginary plane that divides a
crystal into halves, each of which, in a perfectly developed crystal, is the mirror image
of the other (fig. 4).






Mirror Plane = imaginary plane that divides a crystal into halves, each of which is
the mirror image of the other.

(3) Inversion axis: this composite symmetry element combines a rotation about an
axis with inversion through the center (Fig. 5).
(4) Center of symmetry: A crystal is said to have a center of symmetry if an
imaginary line can be passed from any point on its surface through its center and a
similar point is found on the line at an equal distance beyond the center (fig. 6).

Fig. 5: Inversion axis Fig. 6: Center of symmetry

- Symmetry notation: The rotation axes are represented by the numbers 2,3, 4,
and 6 according to whether they are diad, triad, tetrad, and hexad
axes while the corresponding inversion axes have they symbols 2'.., 3', 4'
and 6' respectively. On the other hand the mirror plane is referred to by
latter m and the center of symmetry by 1'.
- Crystal notation: crystallographic axes: they are certain lines passing through
the center of the ideal crystal as axes of reference. These imaginary lines are
called the crystallographic axes and are taken parallel to the intersection edges
of major crystal faces. All crystals, with the exception of these belonging to
the hexagonal and trigonal systems are referred to three crystallographic axes
(fig. 7).

Crystallographic Axes

- CRYSTAL SYSTEMS: on the basis of the symmetry elements, crystals are
grouped into seven major divisions, the seven crystal systems.
Crystal
system
crystallographic
axes
Rotation axes Planes
symmetry
Ex.
Cubic

a = b = c
= = = 90
Four triad axes
/ Four 3-fold :
3- , 4

6

9-planes :


\
6

Pyrite, Halite,
Galena,
Garnet,
Diamond,
Fluorite,Ag
,Cu , crumite

Tetragonal


a = b # c
= = = 90
5 - :
,


5-

Wulfenite,
Rutile, Zircon,
Chalcopyrite

Hexagonal




a1 = a2 = a3 # c
1 = 2 = 3 =
120
, = 90
1-

6



7 :
1- : 6-

Quartz, Beryl
(Emerald),
Apatite,
Corundum
(Ruby,
Sapphire


Trigonal

a1 = a2 = a3 # c
1 = 2 = 3 =
120
, = 90



Calcite,
hematite
,dolomite
Orthorhombic


a # b # c
= = = 90







Sulfur, Barite,
Olivine, Topaz

Monoclinic


a # b # c
= = 90
, # 90







Orthoclase,
Malachite,
Azurite, Mica,
Gypsum
, Talc


Triclinic


a # b # c
# # # 90
-No rotation
axes.



Turquoise,
Kyanite,
Albite,
Plagioclase


Crystal Morphology
A face is designated by Miller indices in
parentheses, e.g. (100) (111) etc.
A form is a face plus its symmetric equivalents
(in curly brackets) e.g {100}, {111}.
A direction in crystal space is given in square brackets e.g. [100],
- Form: the form consist of a group of crystal faces all of which have the same
relation to the elements of symmetry. And display the same chemical and
physical properties because all are underline by the same atoms in the same
geometrical arrangement.
e.g form a is of 4 facies in (fig. 9) and of 6 facies in (fig. 10), form C is of 2 facies
form P of 8 facies, etc.
so that in (fig. 9): a-----4, P-----8, C-----2.
in (fig.10): a-----6, e-----12.


In each crystal classes there is form the faces of which intersects each of the
crystallographic axes at different lengths; this is general form, {hkl}. At other forms
that may be present are special forms.
A crystal form is a crystal face plus its symmetric equivalents. For example, a cube is
a crystal form made up of six symmetrically equivalent faces.
A special form is a crystal form that is repeated by the symmetry operations onto
itself so that there are fewer faces than the order of the point group. The projections of
special forms or special faces will lie on symmetry operations in our stereographic
projections.
A general form is one that is not repeated onto itself by the symmetry operations so
that it has the same number of faces as the order of the group.
Forms are either general or special. In our stereographic projections, we will plot only
the general form because this defines the point group. In addition to being special or
general, forms may also be open or closed.
A closed form is one that encloses a volume; (e.g., a cube, tetrahedron, octahedron,
etc). A closed form may then be the only form present on a perfect crystal.
An open form is one that does not enclose a volume; (e.g., prism, pinacoid, etc.). A
crystal that has an open form must have more than one form present.
Each form of the cubic system has a special name, but the same general names are
used for the forms of the other systems; the following examples are very common:




Pinacoid Prism Pyramids









Scalenohedron Trapezohedrn Pedion
Bipyramids / Dipyramid


Dome or Sphenoid Rhombohedron


- PARAMETERS AND INDICES: crystal faces are defined by indicating
their intercepts on the crystallographic axes (whether its parallel to two axes
and intersects the third, or is parallel to one axis and intersects the other two,
or inter sects all three). In addition one must determine at what relative
distance the face intersects the different axes. The parameters are 1a, 1b, 1c or
1a. 1b, 2c or 1a, 1b, c.
- The indices of the face (the miller indices) are a series of whole numbers
which have been derived from the parameters by their inversion and, if
necessary, the subsequent clearing of fractions. The indices of a face are
always given as three numbers refer to a, b, c or as four numbers refer to a1,
a2, a3, and c.
-
- Examples:
parameters indices


1a, 1b, c (110)
1a, 1b, 2c (22'1)
1a, 1b, c (112)
1a1 = 1a2 = 2a3 , c (2210)

Miller Indices



X =
Y =
Z =



Halite Cube
Miller Indices
Plane cuts axes at intercepts (,3,2).
To get Miller indices, invert and clear fractions.
(1/, 1/3, 1/2) (x6)= (0, 2, 3)
General face is (h,k,l)
Miller Indices
The cube face is (100)
The cube form {100} is comprises faces (100), (010), (001), (100), (0-10), (00-1)

Stereographic Projections.
There are three common methods to graphically display orientations of vectors in
three dimen sions. In order to describe faces of crystals we would like to plot the
vectors normal (perpendicular) to crystal faces.
1. Spherical. The simplest to visualize is the spherical projection. In this method, the
vector is merely projected vertically onto the equatorial plane of the sphere. However,
this method has the serious disadvantage of compressing the low-angle vectors onto
the outside of the plot.
2. Stereographic. This disadvantage can be avoided if, instead of projecting
vertically, one projects radially to the pole of the opposite hemisphere. This is the
standard stereographic or equal-area plot that we will use to plot poles
(perpendiculars) to faces of crystals. The plot is also sometimes called the "Wulff
net". If the angle made by a vector with the vertical is r, then the distance from the
center of the plot is R tan r/2, where R is the radius.

3. Gnomonic. There is also a third type of plot called the gnomonic projection in
which the vector is extended till it intersects a plane tangent to the sphere at the north
pole. This has the disadvantage of not being able to display horizontal vectors. It is,
however, what arises naturally from x-ray and electron diffraction experiments where
each node corresponds to a lattice plane in real space and results in a reciprocal
lattice.
However, for our purposes of displaying the orientations of crystal faces we will use
the stereo graphic projection exclusively.
We will use stereographic projections to plot the perpendicular to a general face and its symmetry equivalents (general
form hkl).


Illustrated above are the stereographic projections
for Triclinic point groups 1 and -1.


CUBIC SYSTEM
Crystallographic Axes: Three axes of equal length that make right angles with
each other.
a = b = c = = = 90

Isometric
System
90 90
90
ISOMETRIC
o = | = = 90
a = b = c
c = a
b = a a
Pyrite, Galena,
Halite, Fluorite,
Garnet, Diamond
o
|

Unique Symmetry:
Four 3-fold axes

Symmetry:
Galena Type
13 rotation axes + 9 mirror planes
3 tetrad crystallographic axes
4 triad diagonal axes
6 diad diagonal axes

Forms:
Six square faces (cube), {001}
8 equilateral triangular faces (octahedron), {111}
12 rhombshaped faces (dodecahedron), {011}
24 isosceles triangular faces (tetrahexahedron), {0kl}
24 trapezium rhombshaped faces (trapezohedron), {hhl}
24 isosceles triangular faces (trioctahedron), {hll}
48 triangular faces (octahexahedron), {hkl}








Forms of Cubic System

Combination of Cubic Forms:
Cube & dodecahedron
Cube & octahedron
Cube, octahedron & dodecahedron
Dodecahedron& octahedron
Octahedron & dodecahedron


Mineral Examples:
Halite, Fluorite, Galena, Diamond, Magnetite, pyrite and gold






TETRAGONAL SYSTEM
Crystallographic Axes: Three axes of that make right angles with each other;
two equal horizontal axes (a, b) with different length
vertical axis (c).



Tetragonal
System
90 90
90
TETRAGONAL
o = | = = 90
a = b = c
c = a
b = a a
Wulfenite, Zircon,
Chalcopyrite, Rutile
o |

Unique Symmetry:
One 4-fold axis

Symmetry:
Zircon Type
a = b # c
= = =
90
One tetrad, 4 diad crystallographic axes and 5 mirror planes (4 vertical + 1
horizontal).

Forms:
4 faces, first order tetragonal prism, {100}
4 faces, second order tetragonal prism, {010}
8 faces, ditetragonal prism, {hk0}
8 faces, first order tetragonal dipyramid {hhl}
8 faces, second order tetragonal dipyramid {0kl}
16 faces, ditetragonal dipyramid {hkl}









Combination of Tetragonal Forms:
~ tetragonal prism & ~ tetragonal dipyramid


Mineral Examples:
Zircon, Cassiterite, ..etc.


HEXAGONAL SYSTEM
Crystallographic Axes:

a1 = a2 = a3 # c

1 = 2 = 3 = 120 ,
= 90

Hexagonal
System
120
90 90
H
E
X
A
G
O
N
A
L
o
=

1
2
0

,

|
=

=

9
0

a

=

b

=
c
c > a
Q
u
a
r
t
z
,

B
e
r
y
l
(
E
m
e
r
a
l d
)
,
A
p
a
t
i t
e
,

G
r
a
p
h
i t
e
,
C
o
r
u
m
d
u
m
(
R
u
b
y
,

S
a
p
p
h
i r
e
)
b = a
o
|
U
n
i q
u
e

S
y
m
m
e
t
r
y
:
O
n
e

6
-
f
o
l d

a
x
i s
a

Symmetry:
Beryl Type

one vertical hexad, 6 horizontal diad crystallographic axes and 7 mirror planes.


Forms:
6 faces, first order hexagonal prism, {101
-
0}
6 faces, second order hexagonal prism, {112
-
0}
12 faces, dihexagonal prism, {hk1
-
0}

12 faces, first order hexagonal dipyramid {h0h
-
l}
12 faces, second order hexagonal dipyramid {hh(2
-
h)l}
24 faces, dihexagonal dipyramid {hk1
-
l}








Combination of Hexagonal Forms:
e.g. Beryl
~ hexagonal prism & ~ hexagonal dipyramid




Mineral Examples:
beryl, molybdenite, pyrrotite, ..etc.



TRIGONAL SYSTEM
Crystallographic Axes:

a1 = a2 = a3 # c

1 = 2 = 3 = 120 , =
90

Symmetry:
Calcite Type
One vertical triad, 3 horizontal diad crystallographic axes and 3 mirror planes
(vertical).




Forms:
(1) Rhombohedron:
6 rhomb-shaped faces, (cube deformed)
Positive rhombohedron, {h0h
-
l} & Negative rhombohedron {0hh
-
l}


(2) Scalenohedron:
12 Scalene triangular faces of a di-hexagonal dipyramid.
The characteristics of the Scalenohedron are the zigzag appearance of the
middle edges which differentials it from the dipyramid, and the alternately
more and less obtuse angles over the edges that meet at the vertices of the
form.
Positive Scalenohedron, {hk1
-
l} & Negative Scalenohedron {kh1
-
l}



Combination of Trigonal Forms:


Mineral Examples:
Calcite, dolomite, magnezite, ..etc.









ORTHOROMBIC SYSTEM
Crystallographic Axes:














Symmetry:
Barytes Type
3 crystallographic axes diad perpendicular to each other and 3 mirror planes
perpendicular to each other.

Forms:
Front Orthorhombic Pinacoid {100}
Side Orthorhombic Pinacoid {010}
Basal Orthorhombic Pinacoid {001}



a # b # c = = = 90
Orthorhombic
System
90 90
90
ORTHORHOMBIC
o = | = = 90
a = b = c
c = a
b = a a
Sulfur, Barite,
Olivine, Topaz
o |

Unique Symmetry:
Three 2-fold axes
4 faces, first order Orthorhombic prism or side dome {0kl}
4 faces, second order Orthorhombic prism or front dome {h0l}
4 faces, third order Orthorhombic prism or vertical Orthorhombic prism {hk0}

5.4a Prism {110} and
pinacoid {001}
5.4b Prism {101} and
pinacoid {010}
5.4c Rhombic prism {011}
and pinacoid {100}

8 faces Orthorhombic dipyramid {hkl}


5.6a Rhombic dipyramid
5.6b
5.6c Sulfur crystal


Combination of Orthorhombic Forms:
~ Orthorhombic prism , ~ Orthorhombic dipyramid &
Orthorhombic Pinacoid

Mineral Examples:
sulfur, staurolite, barite, ..etc.



MONCLINIC SYSTEM
Crystallographic Axes:
a # b # c
Angle between a, b named and
Angle between b, c named = 90
Hence = = 90
Angle between a, c named = >
90 (oblique angle)


Monoclinic
System
90 90
MONOCLINIC
o = = 90, | = 90
a = b = c
c = a
b = a a
O
r
t
h
o
c
la
s
e
,
M
a
la
c
h
it
e
,

A
z
u
r
it
e
,
G
y
p
s
u
m
,

M
ic
a
,

T
a
lc
o
|

Unique Symmetry:
One 2-fold axis
=90

Symmetry:
Gypsum Type
The b axis is rotation diad and a-c
plane is mirror plane.









Forms:
Front Monoclinic Pinacoid {100}
Side Monoclinic Pinacoid {010}
Basal Monoclinic Pinacoid {001}

4 faces, first order Monoclinic prism or side dome
{0kl}
4 faces, second order Monoclinic
prism or front dome {h0l}
4 faces, third order Monoclinic prism
or vertical Monoclinic prism {hk0}
4 faces, fours order Monoclinic prism or Hemi-pyramid {hkl}



Combination of Monoclinic Forms:
~ Monoclinic prism, ~ Monoclinic dipyramid & Monoclinic Pinacoid








NOTE: Figures a, b, and c are common forms for the mineral
orthoclase and d is a common form for selenite (gypsum)
]
Mineral Examples:
gypsum, pyroxene, amphibole, orthoclase. ..etc.






TRICLINIC SYSTEM
Crystallographic Axes:



a # b # c
# # # 90

Triclinic
System
= 9 0
=90
TRICLINIC
o = | = = 90
a = b = c
c = a
T
u
rq
u
o
is
e
, P
la
g
io
c
la
s
e
K
ya
n
ite
, A
lb
ite
o
|

Unique Symmetry:
None
= 9 0
b = a
a

Symmetry:
Axinite Type
one noonad axis of rotation or inversion which is
equivalent to a symmetry center , no axes of
symmetry and no planes of symmetry

Forms:
Front Triclinic Pinacoid {100}
Side Triclinic Pinacoid {010}
Basal Triclinic Pinacoid {001}
2 faces, first order Triclinic prism or side dome {0kl}
2 faces, second order Triclinic prism or front dome {h0l}
2 faces, third order Triclinic prism or vertical Monoclinic prism {hk0}
2 faces, fours order Triclinic prism or Hemi-pyramid {hkl}

Figure 8.3 Triclinic pinacoids, or parallelohedrons



Combination of Triclinic Forms:
~ Triclinic prism, ~ Triclinic dipyramid & Triclinic Pinacoid

Mineral Examples:
plagioclase (feldspars), wallastonite, ..etc.

Crystal Systems
System Axes Angles Unique Symmetry Diagram Examples
Isometric
Tetragonal
Hexagonal
Orthorhombic
Monoclinic
Triclinic


















MINERALOGY
Techniques of mineral identifications
I- Physical Properties in hand specimens (Physical Mineralogy)
II- Optical Properties in petrographic microscope (Optical Mineralogy)
III- Chemical properties (chemistry of minerals and blowpipe test)
IV- Internal structure of crystal of the minerals (x- ray techniques)
I-PHYSICAL PROPERTIES / MINERALOGY
The Physical Properties are very important in the identification of
minerals e.g. 1- Cleavage 2- Parting 3- Fracture 4- Tenacity 5- Specific Gravity
6- Luster 7- Colour 8- Streak 9- Tarnish 10- Magnetism 11- Hardness.
1- Cleavage:
It a mineral, when the proper force is applied, break so that it yields
definite plane surfaces, it is said to possess a cleavage (perfect 1 set or 2
sets.etc or imperfect or lacking ..). Cleavage is dependent on the
crystal structure and takes place only parallel to atomic planes which
have weak binding force between them.
2- Parting:
Twin crystals, especially polysynthetic twins, may separate easily along
the composition planes. When plane surfaces are produced on a mineral
by its breaking along some such predetermined plane, it is said to have a
parting.
3- Fracture:
By the fracture of a mineral is meant the way in which it breaks, when it
does not yield along cleavage or parting surfaces (Conchoidal, Fibrous,
Hackly, Uneven or Irregular).
4- Tenacity:
(Cohesiveness): it is the resistance that a mineral offers to breaking,
crushing, bendin or tearing: Brittle, Malleable, Sactile, Flexible, and
Elastic.



5- Specific Gravity:
Specific Gravity or relative density of a mineral is a number that
expresses the ratio between its weight and the weight of an equal volume
of water at 4c. The Specific Gravity of a crystalline substance is
dependent on:
A- The kind of atoms of which it is composed (atomic wt.).
B- The number in which the atoms are packed together. (Heavy, Moderate,
Light).
6- Luster:
The general appearance of the surface of a mineral in reflected light is
called Luster: Metallic, Sub- Metallic, Non- Metallic (Vitreous, Pearly,
Silky, Greasy, and Adamantine).
7- Colour:
The colour of minerals id one of their most important physical properties
especially those of metallic luster e.g. brass yellow of chalcopyrite. The
change of colour in a mineral is often due to change in composition or to
the presence of impurities.
8- streak:
The colour of the fine powder of a mineral is known as its streak which is
the usually constant for a mineral.
9- Tarnish:
A mineral is said to show a tarnish when the colour of the surface differs
from that of the interior. e.g. in copper minerals (chalcocite, bornite and
chalcopyrite).
10- Magnetism:
The power to attract as possessed by a magnet.
or those minerals that, in their natural state, will be attracted to an iron
magnet are said to be magnetic.
In the magnetic field of a powerful electromagnet many other minerals
containing iron, are drown to the magnet. Because of this, the
electromagnet is an important means of separating mixtures of mineral
grains having different magnetic susceptibilities. (Ex. Magnetite, and less
degree pyrrhotite).
11- Hardness:
(The quality or state of being hard).
The resistance that smooth surface of a mineral offers to scratching is its
hardness.
Hardness like the other physical properties depends on the atomic
structure of the mineral and the difference of binding forces
between the atoms.
Scale of Hardiness
Hardness

1. Talc

2. Gypsum

3. Calcite

4. Fluorite

5. Apatite

6. Orthoclase

7. Quartz

8. Topaz

9. Corundum

10. Diamond


II- OPTICAL MINERALOGY
The branch of mineralogy, which studies minerals under Polarizing
Microscope.

III- CHEMICAL MINERALOGY
(Chemistry of minerals)
"The study of the relationships between chemical composition, internal
atomic structure and physical properties of the mineral"
- Atomic Structure of the minerals:
Minerals are compound of their constituent elements, while rocks are
mixture of their component minerals. Thus the Quartz is a compound (Silica) of
the elements silicon and oxygen.
The proportion of constituent elements of a mineral is represented by a
chemical formula; thus Calcite is composed of calcium, carbon and oxygen in the
proportion of 1:1:3 respectively. The chemical formula can be easily calculated
from chemical analysis of its mineral.
Atomic bonding: there are fore main ways in which may join together:1-
ionic bond (NaCl) 2- covalent bond (Diamond; C) 3- metallic bond (metals)4-
Van der Waals or residual bond( associated with other bonds e.g. Graphite).
More than one type of bond may occur in a single compound (mineral). In
graphite fore example, the carbon atoms are linked in sheets by covalent bond
and the sheets are linked together by Van der Waals bonds.
- Coordination:
In ionic crystals each positive ion (cation) is surrounded by a number of
negative ions (anions), at a distance fixed by the sum of their radii. The number
of anions that can fit around each cation is known as the Coordination number
of cation and termed Kz. The number can be determined by the ratio of the
radius of the cation to that of the anion which expressed by radius ratio. The
different types of Kz are shown in the (Fig.).
RR = radius of cation/radius of anion (usually oxygen)
Radius Ratio (RR)

<0.155
0.155-0.225
0.225-0.414
0.414-0.732
0.732-0.99
1.0
Cation Coord. #

2
3
4
6
8
12
Configuration

linear
trigonal planar
tetrahedral or square
octahedral
cubic
close-packing
(cubic or hexagonal)
Example

CO
2

CO
3
2-

SiO
2

NaCl
CsCl
metals

- isomorphism:
Isomorphous replacement of cations by others of similar size and equal
charge is common in silicates. Thus, Fe
2+
readily replaces Mg
2+
, the two ions
having nearly the same size, and Fe
3+
replaces Al. such replacement is
rondom and results in the minerals concerned variable compositions. The
possibility of isomorphous substitution depends more upon ionic size than
upon valancy. This is well shown by the fact that Na
+
is commonly replaced
by Ca
2+
*as in the plagioclase feldspare), but less readily by K
+
. this is due to
that the Na and Ca ions have almost the same dimensions, whereas the K-
ions is considerably larger than Na. Anions of similar size such as O
2-
, OH
-
, F
-

can also be substituted for one another.
When Si is replaced by Al in 4-fold coordination in silicates, addifference
in ionic charge is involved, since an ion with a lower charge (3+) is substituted
for one with a higher (4+). To make the structure electrically neutral another
cation must be added, so that the sum of the positive charges equals that of
the negative. This isomorphous substitution between elements of different
valency is, therefore, termed coupled atomic substitution.
The plagioclase for example;
Al + Ca replace Si + Na
3 + 2 4 + 1
In which sum of the valence equal 5. this coupled atomic substitution
gives transitional members between the Ca-feldspar (Anorthite) and the Na-
feldspar (albite).
The simplest cases of isomorphous substitution occur when the ions are
equal both in charge and in size, e.g. Mg2+ and Fe2+ as in olivine in which
forsterite ( Mg3SiO4) and fayalite (Fe2 SiO4) are isomorphous. The two
atoms or ions occurring in a mineral are called diadochic if they are capable
of replacing each other in the structure of one mineral and not in another;
each occupying the others position, as in case of Mg2+ and Fe2+ ions in the
olivine structure.
There is usually a limit to the exact to which isomorphous substitution
takes place . the higher temperature of crystallization, gives greater chance of
isomorphus substitution. Increasing rate of crystal growth increases the
chance of isomorphism.
- solid solution and exsolution:
we have observed that most minerals are variable in their composition.
Substitution of one element by another is very common. Any ion in the
structure may be replaced by another ion of similar radius without casing
serious distortion of the structure. When crystals of two components contain
any proportion of the two substance and have unite cell dimensions
intermediate between those of pure components, such crystals are called
mixed crystals or crystalline solid solutions. A solid solution (or mixed
crystal) an be simply defined as a homogeneous crystalline solid of variable
composition. It was early found that many isomorphus substances have the
property of forming solid solution.
Now it is found that many isomorphus substances show little or or no
solid solution (e.g. calcite, CaCo3 and smithsonite, Zn Co3) and extensive
solid solution may occur between substances that are not isomorphus (e.g.
pyrite, FeS and sphalerite, ZnS). On this accunt it must be emphasized that
isomorphism is neither necessary to nor sufficient for solid solution
formation. Isomorphism and solid solution are distinct concepts and should
not be confused.
Since atomic substitution is generally greater at higher temperatures, it
follows that a solid solution formed at high temperature and no longer be
stable at lower temperatures. A solid solution in which two different
elements, A and B are completely inter replaceable at high temperatures but
lower temperatures will tend to break down on cooling into two separate
phases, on rich in A and the other rich in B. this break down of a
homogeneous solid solution id known as exsolution. For example, in the alkali
feldspars K and Na are completely interchangeable at high temperatures; for
any composition in the system KAlSi3O8 - NaAl Si3O8 there is a single
phase solid solution (K, Na)Al Si3O8, which show intermediate unit cell
dimensions Physical Properties. At ordinary temperature the degree of
natural replacement of K and Na in feldspar is quite small, solid solutions of
intermediate composition in this system generally break down, on cooling,
into an intergrowth of Na-rich feldspar and K- rich feldspar known as
perthite.

- defect lattice structures:
The other type of solid solutions is that associated with defect lattices, in
which some of the atoms are missing leaving vacant lattice position. A good
ezample is the mineral pyrrhotite, whose analyses always show more
sulphure than corresponds to the formula FeS. This was, for a long time,
described as solid solution of sulphure in FeS. Actually the excess of sulphure
shown by analyses is the lattice; there is a defectably of Fe not an excess of S.
- pseudomorphism:
Pseudomorphism is the phenomenon of alteration or metasomatic
replacement of crystal of a mineral by other mineral without change of
external form of the original crystal. The new crystal is called pseudomorph
or fals form. Pseudomorphism may be formed in one of the following ways:
a) Paramorphism: in which no change in chemical composition has taken
place e.g. transformation of aragonite (CaCO3, orthorhombic) to calcite (also
CaCO3, trigonal) and rutile to brookite.
b) Substitution: in which there is a gradual removal of the original material
and a responding and simultaneous replacement of two by another with no
chemical reaction between the two, e.g. formation of quartz SiO2 after
fluorite CaF2 and also silica after the wood fibers to petrified wood.
c) Alteration: in which the new mineral has been formed from the original
mineral by a process of chemical alteration may originate by:
1. The loss of a constituent (e.g. change of magnetite, Fe3O4 to hematite,
Fe2O3 by loss of Fe).
2. The gain (addition) of a constituent (e.g. change of anhydrite, CaSO4
to gypsum, CaSO4.2H2O by addition of H2O) and malachite after
cuprite.
3. A partial exchange of constituents (e.g. goethite, HFeO3 after pyrite,
FeS2 by loss of S and addition of H2O
- polymorphism:
An element or compound that can exist in more than one crystal form is
said to be isomorphus, each form has different physical properties and a
distinct crystal structure.
The new form of the same chemical composition is formed as a result of
changes in temperatures, pressure and chemical environment.
A polymorphism substance may be described as dimorphic/trimorphic
are depending to the number of distinct crystalline forms the substance is an
element, the polymorphism is termed allotropy, e.g. carbon which occurs as
graphite ( hexagonal) and diamond (cubic).
Two types of polymorphism are recognized, according whether the
change from one polymorph to another is reversible and takes place at a
definite temperature and pressure; is known as anantiotropy, or is
irreversible and does not take place at a definite temperature and pressure
and termed monotropy.





Examples of anantiotropic polymorphism
Quartz
(SiO2)
870C

Tridymite
(SiO2)
1470C

Cristobalite
(SiO2)
Triagonal Hexagonal Cubic

Brookite
(TiO2)
900 C

Anatase
(TiO2)
900 C

Rutile
(TiO2)
Orthorhombic Tetragonal Tetragonal





Examples of Monotropypolymorphism

Marcasite (FeS)

Pyrite (FeS)
Orthorhombic Cubic

Diamond (C)

Graphite (C )
Cubic hexagonal

3. Bond Types in Crystals
Bonds are electrical forces that bind atoms in crystalline solids. Largely control
physical properties (hardness, cleavage, melting T, and conductivity). Four major
types. Most minerals in fact are combinations of the four types. Silicates are mostly
ionic/covalent with some having weak van der Waals/hydrogen bonds as well. For
example, MICAS: within sheets bonding is 50-50 ionic/covalent; bonds between
sheets are mostly weak ionic and/or van der Waals.
- Ionic: One or more electrons are transferred to the outer shell of another
element so they both have filled outer shells (inert configuration). Halite is
Na+, Cl-; have electrical attraction that produces IONIC BOND. Physical
properties of minerals with ionic bonds: soluble, moderate hardness and G,
fairly high melting T, poor conductors of heat and electricity. Strength of ionic
bonding is proportional to 1/r and q1q2, where r is interatomic distance
between ions and q1, q2 is the valence of the two ions.
- Covalent (strongest chemical bond): One or more electrons are shared in outer
shells of two atoms to produce the inert electronic configuration. Physical
properties of minerals with covalent bonds: insoluble, stable, moderate to very
high hardness, very high melting T, poor electrical conductors.
- Metallic: Forces that arise from atoms that share electrons that from a cloud
of e
-
around the atoms. No e
-
has affinity to any one atom and is free to move
around in structure. Physical properties of minerals with metallic bonds: soft,
high plasticity, maleable, very conductive.
- van de Waals: Polarization of atoms causes a weak dipolar attraction. Can
bond together neutral molecules and essentially uncharged structural units by
developing small electrostatic forces on surfaces. Defines zones of cleavage,
and low hardness in some minerals (clays, micas).


-
-
- X-ray Diffraction Analysis and other Techniques
Nature and production:

Prof. Gorring
GEOS 443 MINERALOGY
Oct. 22, 1998
X-Ray Diffraction
1. X-Ray Spectra
X-Rays are only a small part of the electromagnetic spectum with wavelengths ()
ranging from 0.02 A to 100 A (A = Angstroms = 10
-8
m). X-Rays used to study
crystals have on the order of 1 to 2 A (i.e. Copper Ko = 1.5418 A). Visible light
has much larger 's (4000-7200 A) and thus, x-rays are much more energetic (i.e. can
penetrate deeper into a material). This can easily be seen by inspection of the
Einstein equation (E = hv = hc/; E is Energy, v frequency, c speed of light which is
constant for electromagnetic radiation, wavelength, h Plank's constant).

2. Diffraction and the Bragg Equation
- Diffraction of an x-ray beam striking a crystal occurs because the of the x-
ray beam is similar to the spacing of atoms in minerals (1-10 A). When an
x-ray beam encounters the regular, 3-D arrangement of atoms in a crystal most
of the x-rays will destructively interfere with each other and cancel each other
out, but in some specific directions they constructively interfere and
reinforce one another. It is these reinforced (diffracted) x-rays that produce
the characteristic x-ray diffraction patterns that used for mineral ID.
W.L. Bragg (early 1900's) showed that diffracted x-rays act as if they were
"reflected" from a family of planes within crystals. Bragg's planes are the rows of
atoms that make up the crystal structure. These "reflections" were shown to only
occur under certain conditions which satisfy the equation:

n = 2dsin (Bragg Equation)
where n is an interger (1, 2, 3, ......, n), the wavelength, d the distance between
atomic planes, and u the angle of incidence of the x-ray beam and the atomic planes.
2dsinu is the path length difference between two incident x-ray beams where one x-
ray beam takes a longer (but parallel) path because it "reflects" off an adjacent atomic
plane. This path length difference must equal an integer value of the of the incident
x-ray beams for constructive interference to occur such that a reinforced diffracted
beam is produced.

- For a given of incident x-rays and interplanar spacing (d) in a mineral, only
specific u angles will satisfy the Bragg equation. Example: focus a monochromatic
x-ray beam (x-rays with a single ) on a cleavage fragment of calcite and slowly
rotate crystal. No "reflections" will occur until the incident beam makes an angle u
that satisfies the Bragg equation with n = 1. Continued rotation leads to other
"reflections" at higher values of u and correspond to when n = 2, 3, ... etc.; these
known as 1st, 2nd, 3rd order, etc., "reflections".
3. X-Ray Diffraction Techniques
- Photographic plates were traditionally used to record the intensity and position
of diffracted x-rays. Modern systems use diffractometers which are electronic
x-ray counters (detectors) that can measure intensities much more accurately.
Computers are used to process data and make necessary complex calculations.
- There are two main techniques.
o Single-Crystal Methods: (x-ray beam is focused on a single crystal).
Primary application is to determine atomic structure
(symmetry, unit cell dimensions, space group, etc.,).
Older methods (Laue method) used a stationary crystal with
"white x-ray" beam (x-rays of variable ) such that Bragg's
equation would be satisfied by numerous atomic planes. The
diffracted x-rays exiting the crystal all have different u and thus
produce "spots" on a photographic plate. The diffraction spots
show the symmetry of the crystal.
Modern methods (rotation, Weissenberg, precession, 4-circle)
utilize various combination of rotating-crystal and camera setup
to overcome limitations of the stationary methods (mainly the #
of diffractions observed). These methods use monochromatic
x-rays, but vary u by moving the crystal mounted on a rotating
stage. Usually employ diffractometers and computers for data
collection and processing.
o Powder Methods: (x-ray beam focused on a powder pellet or powder
smeared on a glass slide). Essential for minerals that do not form large
crystals (i.e. clays) and eliminates the problem of precise orientation
necessary in single-crystal methods.
Primary application is for mineral identification. Also can be
used to determine mineral compositions (if d-spacing is a
function of mineral chemistry) and to determine relative
proportions of minerals in a mixture.
Monochromatic x-rays are focused on pellet or slide mounted
on rotating stage. Since sample is powder, all possible
diffractions are recorded simultaneously from hypothetical
randomly oriented grains. Mount is then rotated to ensure all
diffractions are obtained.
Older methods used photographic techniques. Most modern
applications employ X-Ray Powder Diffractometers.
4. X-Ray Powder Diffractometry
- Uses monochromatic x-rays on powder mounted on glass slide that is attached
to a stage which systematically rotates into the path of the x-ray beam through
u = 0 to 90.
- The diffracted x-rays are detected electronically and recorded on a inked strip
chart. The detector rotates simultaneously with the stage, but rotates through
angles = 2u. The strip chart also moves simultaneously with the stage and
detector at a constant speed.
- The strip chart records the intensity of x-rays as the detector rotates through
2u. Thus, the angle 2u at which diffractions occur and the relative intensities
can be read directly from the position and heights of the peaks on the strip
chart.
- Then use the Bragg equation to solve for the interplanar spacings (d) for all the
major peaks and look up a match with JCPDS cards. JCPDS = Joint
Committee on Powder Diffraction Standards.



CLASIFICATION OF MINERALS

We can classify the minerals into nine groups according to their chemical
compositions; these groups are:

1. Native elements.
The importants native elements are classified as follows:
A- Trace metals consist of large number of crystals, each of which is
composed of closely packed atoms of the particular metallic element. Such a
crystal may be considered as an aggregate of positive ions immersed in gas "or"
cloud" of free electrons and attracted together by metallic bonding.
Many properties which are characteristic of metals, such as their opaqueness
and conductivity of heat and electricity' are due o the presence of the free
electrons. Examples: Gold, Silver, Copper, Iron, Nickel.
B- Semimetals (carbon group) which includes tow natural forms of carbon,
diamond and graphite. Diamond is isometric with each carbon atom linked
tetrahedrally (covalent bonding) to four neighboring carbon atoms. In graphite
on the other hand, the carbon atoms lie in layers or sheets. Each sheet is covalent
bond together and every to sheets linked by Van Der Waals (weak) bond.



2. Sulphides
Sulphides include a large group of minerals, with the general formula A
m

X
p
, in which X is Sulpher and A is the smaller metal atom. Examples: Galena
(PbS), Chalcopyrite (CuFeS
2
), Pyrite (FeS
2
) and .etc.

3. Oxides
This large class of minerals includes those compounds in which atoms or
cations, usually of one or more metals, are combined with oxygen that have ionic
bonding. Examples: Magnetite (Fe
3
O
4
), Chromite (Mg,Fe) Cr
2
O
4
, Hematite
(Fe
2
O
3
), Ilmenite (Fe TiO
3
), Rutile (TiO
2
) and Cassiterite (SnO
2
).


4. Hydroxides
They have a layer structure in which each layer, parallel to (0001),
consists of two sheets of Oh with a sheet of Mg or Fe or Al atoms between them.
Examples: Brucite (Mg (OH)
2
), and Gibbsite (Al(OH)
3
).

5. Halides.
The halides comprise those minerals which are primarily compounds of
the halogen elements (F, Cl, Br, I). Examples: Halite (NaCl) and Fluorite (CaF
2
).

6. Carbonates
The carbonates include some very common and widespread minerals in
which the fundamental anionic unit is (CO
3
)
2-
.
Examples: Calcite (CaCO
3
), Dolomite (Ca, Mg (CO
3
)
2
), Aragonite (CaCO
3
),
Magnesite (MgCO
3
), Siderite (FeCO
3
), Witherite (BaCO
3
).

7. Sulphides
They comprise a large number of minerals; some of which are anhydrous
e.g. Barite

8. Phosphates
This group of minerals includes a large number of naturally occurring
oxysalts with an ionic group of (PO
4
)
3-
Examples: Monazite ((Ce, La, Y, Th) PO
4
)
and Apatite (Ca
5
(PO
4
)
3
F, Cl).

9. Silicates
The silicates minerals are of greater importance than any other (nearly
$0% of the common minerals are silicates). The powerful bonds between the
oxygen and silicon ions are 50% ionic and 50% covalent.
In all silicate structures, the fundamental unit in the building of silicate minerals
is situated at the center of a tetrahedron whose corners are occupied by four
oxygen atoms.
Classification of the silicates is based on the different ways which the
SiO4 tetrahedra occur, either separately or linked together. On this basis we can
differentiate between 6 subgroups as given in the following table.

Structural Classification of Silicates
Subgroup
Structure
arrangement
Si:O
Ratio
Examples
Nesosilicates
single tetrahedrons
(no Oxygens. shared
between
neighboring
tetrahedra) joined
by bonds with other
cations
1:4
Olivine
(Fe,Mg)
2
SiO
4
Garnet
(Ca,Fe,Mg)
3
(Al,Cr,Fe)
2
(SiO
4
)
3

Sorosilicates
two tetrahedra
sharing one
Oxygens.
2:7
Epidote
Ca
2
Al
2
(FeO)(SiO
4
)(Si
2
O
7
)(OH)
Hemimorphite
Zn
4
Si
2
O
7
(OH)
2
.H
2
O
Cyclosilicates
Closed rings of
tetrahedra each
sharing 2 Oxygens.
1:3
Tourmaline
(Na,Ca)(Li,Mg,Al)(Al,Fe,Mn)
6
(BO
3
)
3
(Si
6
O
18
)(OH)
4

Beryl
Be
3
Al
2
Si
6
O
18

Inosilicates
Single Chain
Continuous single
chains
of tetrahedra
sharing 2 oxygens.
1:3
Amphiboles
Anthophylite
Mg
7
(Si
4
O
11
)
2
(OH)
2
Hornblende
(Ca,Na)
2-3
(Mg,Al,Fe)
5
Si
6
(Si,Al)
2
O
22
(OH)
2

Inosilicates
Double Chain
Continuous double
chains
of tetrahedra
sharing alternatively
2 then 3 oxygens.
4:11
Pyroxene
Enstatite
MgSiO
3

Phyllosilicates
Continuous sheets
of tetrahedron
each sharing 3
oxygens.
2:5
Dioctahedral: Muscovite
KAl
2
(Si
3
Al
1
)O
10
(OH)
2

Trioctahedral: Talc
(Mg,Fe)
3
Si
4
O
10
(OH)
2

Tectosilicates
Continuous
framework
of tetrahedra each
sharing all 4
oxygens.
1:2
Quartz - SiO
2


STRUCTURAL CLASSIFICATION OF SILICATES
1- Neosilcates
Neosilicates are those silicates with isolated (SiO
4
)
4-
groups in the
structure which are bound by cations only (ionic bonds). e.g. Olivine group,
Garnet Group, Aluminum Silicate group (Andalusite, Sillimanite, Kyanite and
Staurolite) and Zircon and Sphene.
Structure of Olivine (Mg, Fe)
2
SiO
4
is shown in ( Fig. 37) as example.
2- Sorosilicates
In the sorosilicates two SiO
4
tetrahedra are linked by sharing one
oxygen, forming (Si
2
O
7
)
6-
group in the structure (e.g Epidote and
Hemimorphite).
3- Cyclosilicates
The cyclosilicates are so named because they contain rings of linked SiO4
tetrahedra on either side, giving formula (SiO3)
-2
n e.g. Tourmaline.

4- Inosilicates
The inosilicates are a subclass in which the SiO
4
tetrahedra are linked to
form chains of indefinite extent. There are two main types of chain structure.
A- Pyroxene Group being single chain structures e.g. Enstatite and
Hypersthene (orthorhombic) and Diopside, Augite and Aegirine
(monoclinic) producing composition (SiO
3
)
2-

Structure of diopside (Ca Mg Si
2
O
6
) is shown in (Fig. 40).
B- Amphibole Group being double chain structure. e.g. Anthophyllite
C- (Orthorombic) and Tremolite, Actinolite, Hornblend, Riebeckite
(monoclinic).
Structure of Tremolite (Ca
2
Mg
5
Si
8
O
22
(OH)
2
) is shown in (Fig. 41).
- Cleavage of Pyroxene and Amphibole (Fig. 38 and 39). The bonding
between the chains is weaker than the bonding within the chains
themselves, and as a result both the pyroxenes and the amphiboles
have good prismatic cleavage (Fig. 38). The chains have trapezium-
shaped cross- sections (Fig. 39), the length of the which in the (b)
direction is double as in the amphibole as in the pyroxene. Cleavage
takes place in a diagonal manner, avoiding cutting through the chains
(broken line).

Properties Pyroxene Amphibole
b-dimension
b-dimension is ~9 ; 1/2 that
of amphiboles
b-dimension is ~18 ; 2x that of
pyroxenes
Chem. Comp.
no OH
-
in structure (Not
contain OH
-
group)
OH
-
in structure(contain OH
-

group)
Form
Generally blocky, prismatic
crystal habit
(Short prismatic crystal)
elongate, splintery, acicular (rod
shaped) habit
(long prismatic crystal)
Cross Section 8- sided 6- sided
Cleavage Angle 90 degree cleavage 60-120 cleavage
Extinction angle
Large; 53 - 55 (except
soda types)
Small; 15 - 25 (except soda
types)
Colour weak Strong
Pleochrism weak Strong
Alteration
Altered to amphiboles Altered to chlorite and other micas
Mode of
occurrence
They are present in basic and
ultrabasic igneous rocks and
are less abundant in
metamorphic rocks (high
grade)
They are more common in
intermediate igneous rocks and
metamorphic rocks (medium
grade)
Temperature
form at high temperatures form at lower T than pyroxenes
Unit cell
dimintions
a b c
9.73 8.91 5.25
a b c
9.74 17.8 5.26
Si : O ratio
No Present of OH
-

Si : O = 1 : 3
Present of OH
-

Si : O = 4 : 11
= Angstroms = 10
-8
cm.

5- Phyllosilicates
The basic structural features of al minerals in this subclass is the presence
of SiO
4
tetrahedra linked by sharing three of the 4-oxygens to form sheets with a
pseudohexagonal network. This sheets called tetrahedral layers of (Si
4
O
10
)
6-
.
sometimes Al replace Si giving sheets of (AlSi
4
O
10
)
5-
and (Al
2
Si
4
O
10
)
6-
.
In all phyllosilicates this tetrahedral layer id combined with another sheet
like grouping of cations( usually Al, Mg, or FeO in six-coordination with
Oxygen and Hydroxyl anions. six-coordination means that the anions are
arranged around the cations in an octahedral pattern, one anion at each solid
center of an octahedron and a cation at the center. By the sharing of anions
between adjacent octahedral a planer network results, and this is often known as
octahedral layer which has two surfaces or two sides (remember that octahedral
refers to the arrangement of the anions, not their number).
The mineral Gibbsite, Al (OH)
3
and Brosite Mg (OH)
2
(Fig.--), have this
type of structure, and the Al-OH layers and Mg-OH layers and Brosite layers,
respectively. The Gibbsite layer has dioctahedral arrangement, that is their
being three cations for each six OH anions.
The dimensions of the tetrahedral and the octahedral layers are closely
similar, and consequently, compose tetrahedral- octahedral layers are readily
formed either one tetrahedral and one octahedral layer (a two layer layers), or
an octahedral layer sandwiched between two tetrahedral layers (a three-
structure). Therefore, if only one surface of an octahedral layer is shared with a
tetrahedral layer, a two layer mineral results (e.g. kaolinite, Fig. 45); if both
surfaces are shared, a three layer is obtained (e.g. muscovite, Fig. 43).
Muscovite structure, KAl
2
(Al Si
3
) O
10
(OH)
2
As shown in Fig. 43, in the muscovite structure, on silicon of Si
4
O
10
layers
is replaced by Al, and this increases the negative charge in the layers which is
balanced by the addition of positive ions (K) between the layers. The (Al Si
3
) O
10
sheets (tetrahedral layer) are arranged in pairs, with the apexes of their linked
tetrahedral pointing inwards in each pair (Fig.43).
The two sheets of a pair are linked together by Al cations which lie
between them. Each Al is octahedrally coordinated by 4-Oxygens belonging to
the two sheets and 2-OH. On the other hand, between on pair of sheets and the
next pair (between the bases of tetrahedra) lie the K ions, which are in 12-
coordination. This K-O bond is a much weaker bond (Van Der Waals bond)
than the other bonds in the structure, and the perfect cleavage for which mica is
noted takes place along the layers of K ions, parallel to the sheet structure
muscovite is monoclinic.
The composite octahedral - tetrahedral layers are always staked in the
direction of the c axis in the crystal, in a, b plane the crystals are
pseudohexagonal symmetry. As shown in Fig. 44, the hexagonal symmetry of
each individual sheet is lost when two sheet are opposed to form a double sheet
(pair of sheets); linked by Al. the hexad axis of each single sheet passes through
the OH groups and since these to a pair of sheets, and the symmetry is lowered to
monoclinic.
6- Tectosilicates (Framwork)
Tectosilicates includes some of the most important rock-forming
minerals, e.g. Quartz., Feldspars and Feldspathoide. Except quartz, all minerals
of the tectosilicates are aluminosilicatea in which Al replaces some of the Si in
tetrahedra to form excess negative charge. The cations which balance the
negative charge on the structure are always large ions (e.g. K, Na and Ca) with
coordination 8 or more and never smaller 6- coordination cation (e.g. Mg & Fe).
Slica group
Silica occurs in nature as three common minerals quartz, tridymite and
cristobalite Fig. 47.
Feldspars
The feldspars are the most abundant of all minerals. They are closely
related in form and physical properties, but they fall into two subgroups. The K-
Feldspars which are; monoclinic and the Na and Ca Feldspars (the plagioclases)
which are triclinic.
The general formula for the Feldspars Can be written W Z
4
O
8
, in which
W, may be; Na, K, Ca and Z, is Si and Al, the Si:Al ratio varying from 3:1 to 1:1.
4 point of great interest is the isomorphism between albite, NaAlSi
3
O
8
and
anorthite CaAl
2
Si
2
O
8
of plagioclase series. The following species are recognized:
K- Feldspar:
Sandine, KAlSi
3
O
8

Orthoclase, KAlSi
3
O
8

Microcline, KAlSi
3
O
8

plagioclase series:
Albite, (Ab)NaAlSi
3
O
8

Oligioclase, Ab
6
An to Ab
3
An
Andesine, Ab
3
An to Ab An
Labradorite, Ab An to Ab An
3

Bytownite, Ab An
3
to Ab An
6

Anorthite, (An) CaAl
2
Si
2
O
8


The structure of feldspars is a continuous three-dimensional
network of SiO
2
and AlO
4
tetrahedra with the positively charged Na, K
and Ca situated in the interstices of the negatively charged network.